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C语言实现Huffman树并计算带权路径长度

2015-09-16 20:32 381 查看
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#include<stdio.h>
#include<stdlib.h>
typedef int ElemType;
typedef struct _BTreeNode 
{
    ElemType data;
    struct _BTreeNode* left;
    struct _BTreeNode* right;
}BTreeNode;

//根据数组 a 中 n 个权值建立一棵哈夫曼树,返回树根指针
BTreeNode* CreateHuffman(ElemType a[], int n)
{
    int i, j;
    BTreeNode **b, *q;
    b = (BTreeNode **)malloc(n*sizeof(BTreeNode));
    for (i = 0; i < n; i++) //初始化b指针数组,使每个指针元素指向a数组中对应的元素结点
    {
        b[i] =(BTreeNode *) malloc(sizeof(BTreeNode));
        b[i]->data = a[i];
        b[i]->left = b[i]->right = NULL;
    }
    for (i = 1; i < n; i++)//进行 n-1 次循环建立哈夫曼树
    {
        //k1表示森林中具有最小权值的树根结点的下标,k2为次最小的下标
        int k1 = -1, k2;
        for (j = 0; j < n; j++)//让k1初始指向森林中第一棵树,k2指向第二棵
        {
            if (b[j] != NULL && k1 == -1)
            {
                k1 = j;
                continue;
            }
            if (b[j] != NULL)
            {
                k2 = j;
                break;
            }
        }
        for (j = k2; j < n; j++)//从当前森林中求出最小权值树和次最小
        {
            if (b[j] != NULL)
            {
                if (b[j]->data < b[k1]->data)
                {
                    k2 = k1;
                    k1 = j;
                }
                else if (b[j]->data < b[k2]->data)
                    k2 = j;
            }
        }
        //由最小权值树和次最小权值树建立一棵新树,q指向树根结点
        q =(BTreeNode *) malloc(sizeof(BTreeNode));
        q->data = b[k1]->data + b[k2]->data;
        q->left = b[k1];
        q->right = b[k2];

        b[k1] = q;//将指向新树的指针赋给b指针数组中k1位置
        b[k2] = NULL;//k2位置为空
    }
    free(b); //删除动态建立的数组b
    return q; //返回整个哈夫曼树的树根指针
}

ElemType WeightPathLength(BTreeNode* FBT, int len)//len初始为0
{
    if (FBT == NULL) //空树返回0
        return 0;
    else
    {
        if (FBT->left == NULL && FBT->right == NULL)//访问到叶子结点
            return FBT->data * len;
        else //访问到非叶子结点,进行递归调用,返回左右子树的带权路径长度之和,len递增
            return WeightPathLength(FBT->left,len+1)+WeightPathLength(FBT->right,len+1);
    }
}

//主函数
void main()
{
    int n, i;
    ElemType* a;
    BTreeNode* fbt;

    while(1)
    {
        scanf("%d", &n);
        if (n > 1)
            break;
        else
            printf("重输n值:");
    }
    a =(int *) malloc(n*sizeof(ElemType));
   
    for (i = 0; i < n; i++)
        scanf(" %d", &a[i]);
    fbt = CreateHuffman(a, n);
    printf("%d\n", WeightPathLength(fbt, 0));
    
    
}
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